# Convergent series

Use

1) sum of (x ^ (n +1))/ (n +1 ) converges uniformly

on [-1, 0]

2) sum of x ^ n converges uniformly on (-1, 0]

3) sum of x ^ n = 1/(1-x)

to show that ln 2 = 1 - 1/2 + 1/3 - 1/4 ...

Â© BrainMass Inc. brainmass.com March 4, 2021, 5:58 pm ad1c9bdddfhttps://brainmass.com/math/calculus-and-analysis/convergent-series-natural-log-series-21352

#### Solution Preview

Solution in attached file (soln_21352.doc)

Problem:

ln 2 = 1 - 1/2 +1/3 - 1/4 ...

use ...

#### Solution Summary

This solution looks at the convergent natural log series.

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